We do not say that it produces complexity, but that it "is" complex. Evolution is the one that say it produces higher and more complex life forms. Without the assumption that only intelligence can produce SC, ID hasn't a leg to stand on.
All we have to prove is that something couldn't have been been made by shear chance. Believing that you are a product of sheer chance is a pretty good trick you know when you consider the complexity of your body, immune system, brain and DNA.
Using the same logic of evolution and chance, one could be able to say that a Toyota Hybrid was produced by bacterium, not man. Sometimes we need to look at the whole picture and say it is too complex for chance to have done it.
And when we finally admit that chance is too great, we will look at it for life's complexity and make greater scientific advancements than to claim that it is not complex and not intricate.
Sorry, IMHO, evolution will be swept away by sheer amounts of information about the complexity and logic in life (doubling every year) and that it is too intricate to be produced only by sheer chance.
That's often given as an explanation of earthquakes.